讲座内容：

For a connected graph G, a spanning tree T of G is called a homeomorphically irreducible spanning tree (HIST) if T has no vertices of degree 2. In this talk, we show that if G is a graph of order n≥270 and |N(u)\cup N(v)|≥(n-1)/2 holds for every pair of nonadjacent vertices u and v in G, then G has a HIST, unless G belongs to three exceptional families of graphs or G has a cut-vertex of degree 2. This result improves the latest conclusion, due to Ito and Tsuchiya, that a HIST in G can be guaranteed if d(u) + d(v)≥n-1 holds for every pair of nonadjacent vertices u and v in G.